33 research outputs found
Entropy generation in 2+1-dimensional Gravity
The tunneling approach, for entropy generation in quantum gravity, is shown
to be valid when applied to 3-D general relativity. The entropy of de Sitter
and Reissner-Nordstr\"om external event horizons and of the 3-D black hole
obtained by Ba\~nados et. al. is rederived from tunneling of the metric to
these spacetimes. The analysis for spacetimes with an external horizon is
carried out in a complete analogy with the 4-D case. However, we find
significant differences for the black hole. In particular the initial
configuration that tunnels to a 3-D black hole may not to yield an infinitely
degenerate object, as in 4-D Schwarzschild black hole. We discuss the possible
relation to the evaporation of the 3-D black hole.Comment: 22 pages, Tex, TAUP-2102-9
Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time
A formalism for quantizing time reparametrization invariant dynamics is
considered and applied to systems which contain an `almost ideal clock.'
Previously, this formalism was successfully applied to the Bianchi models and,
while it contains no fundamental notion of `time' or `evolution,' the approach
does contain a notion of correlations. Using correlations with the almost ideal
clock to introduce a notion of time, the work below derives the complete
formalism of external time quantum mechanics. The limit of an ideal clock is
found to be closely associated with the Klein-Gordon inner product and the
Newton-Wigner formalism and, in addition, this limit is shown to fail for a
clock that measures metric-defined proper time near a singularity in Bianchi
models.Comment: 16 pages ReVTeX (35 preprint pages
Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?
It is stated that holonomy corrections in loop quantum cosmology introduce a
modification in Friedmann's equation which prevent the big rip singularity.
Recently in \cite{h12} it has been proved that this modified Friedmann equation
is obtained in an inconsistent way, what means that the results deduced from
it, in particular the big rip singularity avoidance, are not justified. The
problem is that holonomy corrections modify the gravitational part of the
Hamiltonian of the system leading, after Legendre's transformation, to a non
covariant Lagrangian which is in contradiction with one of the main principles
of General Relativity. A more consistent way to deal with the big rip
singularity avoidance is to disregard modification in the gravitational part of
the Hamiltonian, and only consider inverse volume effects \cite{bo02a}. In this
case we will see that, not like the big bang singularity, the big rip
singularity survives in loop quantum cosmology. Another way to deal with the
big rip avoidance is to take into account geometric quantum effects given by
the the Wheeler-De Witt equation. In that case, even though the wave packets
spread, the expectation values satisfy the same equations as their classical
analogues. Then, following the viewpoint adopted in loop quantum cosmology, one
can conclude that the big rip singularity survives when one takes into account
these quantum effects. However, the spreading of the wave packets prevents the
recover of the semiclassical time, and thus, one might conclude that the
classical evolution of the universe come to and end before the big rip is
reached. This is not conclusive because. as we will see, it always exists other
external times that allows us to define the classical and quantum evolution of
the universe up to the big rip singularity.Comment: Accepted for publication in JCA
Tomographic entropy and cosmology
The probability representation of quantum mechanics including propagators and
tomograms of quantum states of the universe and its application to quantum
gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator,
free pointlike particle and repulsive oscillator are considered. The notion of
tomographic entropy and its properties are used to find some inequalities for
the tomographic probability determining the quantum state of the universe. The
sense of the inequality as a lower bound for the entropy is clarified.Comment: 19 page
The Problem of Time and Quantum Black Holes
We discuss the derivation of the so-called semi-classical equations for both
mini-superspace and dilaton gravity. We find that there is no systematic
derivation of a semi-classical theory in which quantum mechanics is formulated
in a space-time that is a solution of Einstein's equation, with the expectation
value of the matter stress tensor on the right-hand side. The issues involved
are related to the well-known problems associated with the interpretation of
the Wheeler-deWitt equation in quantum gravity, including the problem of time.
We explore the de Broglie-Bohm interpretation of quantum mechanics (and field
theory) as a way of spontaneously breaking general covariance, and thereby
giving meaning to the equations that many authors have been using to analyze
black hole evaporation. We comment on the implications for the ``information
loss" problem.Comment: 30 pages, COLO-HEP-33
Quantum Gravity and Turning Points in the Semiclassical Approximation
The wavefunctional in quantum gravity gives an amplitude for 3-geometries and
matter fields. The four-space is usually recovered in a semiclassical
approximation where the gravity variables are taken to oscillate rapidly
compared to matter variables; this recovers the Schrodinger evolution for the
matter. We examine turning points in the gravity variables where this
approximation appears to be troublesome. We investigate the effect of such a
turning point on the matter wavefunction, in simple quantum mechanical models
and in a closed minisuperspace cosmology. We find that after evolving
sufficiently far from the turning point the matter wavefunction recovers to a
form close to that predicted by the semiclassical approximation, and we compute
the leading correction (from `backreaction') in a simple model. We also show
how turning points can appear in the gravitational sector in dilaton gravity.
We give some remarks on the behavior of the wavefunctional in the vicinity of
turning points in the context of dilaton gravity black holes.Comment: 32 pages, 3 Postscript figures, uses epsf.tex and fps.sty, some
discussion, references and Acknowledgements added, version to appear in Phys.
Rev.
Particle creation in a tunneling universe
An expanding closed universe filled with radiation can either recollapse or
tunnel to the regime of unbounded expansion, if the cosmological constant is
nonzero. We re-examine the question of particle creation during tunneling, with
the purpose of resolving a long-standing controversy. Using a perturbative
superspace model with a conformally coupled massless scalar field, which is
known to give no particle production, we explicitly show that the breakdown of
the semiclassical approximation and the ``catastrophic particle production''
claimed earlier in the literature are due to an inappropriate choice of the
initial quantum state prior to the tunneling.Comment: 21 pages, 3 embedded figures, RevTeX
Quantum geometrodynamics: whence, whither?
Quantum geometrodynamics is canonical quantum gravity with the three-metric
as the configuration variable. Its central equation is the Wheeler--DeWitt
equation. Here I give an overview of the status of this approach. The issues
discussed include the problem of time, the relation to the covariant theory,
the semiclassical approximation as well as applications to black holes and
cosmology. I conclude that quantum geometrodynamics is still a viable approach
and provides insights into both the conceptual and technical aspects of quantum
gravity.Comment: 25 pages; invited contribution for the Proceedings of the seminar
"Quantum Gravity: Challenges and Perspectives", Bad Honnef, Germany, April
200
Topology, Decoherence, and Semiclassical Gravity
We address the issue of recovering the time-dependent Schr\"{o}dinger
equation from quantum gravity in a natural way. To reach this aim it is
necessary to understand the nonoccurrence of certain superpositions in quantum
gravity.
We explore various possible explanations and their relation. These are the
delocalisation of interference terms through interaction with irrelevant
degrees of freedom (decoherence), gravitational anomalies, and the possibility
of states. The discussion is carried out in both the geometrodynamical
and connection representation of canonical quantum gravity.Comment: 18 pages, ZU-TH 3/93, to appear in Phys. Rev.
Breakdown of the semiclassical approximation at the black hole horizon
The definition of matter states on spacelike hypersurfaces of a 1+1
dimensional black hole spacetime is considered. The effect of small quantum
fluctuations of the mass of the black hole due to the quantum nature of the
infalling matter is taken into account. It is then shown that the usual
approximation of treating the gravitational field as a classical background on
which matter is quantized, breaks down near the black hole horizon.
Specifically, on any hypersurface that captures both infalling matter near the
horizon and Hawking radiation, quantum fluctuations in the background geometry
become important, and a semiclassical calculation is inconsistent. An estimate
of the size of correlations between the matter and gravity states shows that
they are so strong that a fluctuation in the black hole mass of order
exp[-M/M_{Planck}] produces a macroscopic change in the matter state.Comment: Latex, 31 pages + 5 uuencoded figure